Toroidal confinement plasma devices are devices in which a toroidal plasma is created in the space of a vessel which may be topologically that of a torus or of a cylinder, usually axisymmetric, and is confined therein by appropriate confining magnetic fields. Toroidal plasma devices are useful in the generation, confinement and heating, and study and analysis of plasmas. In particular, these devices are useful for reacting deuterium and tritium, deuterium and deuterium or other nuclear fusible mixtures, with the production of high energy neutrons and energetic charged particles as products of the nuclear fusion reactions.
At large, the problems in nuclear fusion devices are heating a dense enough plasma to a high enough temperature to enable the desired reactions to occur and confining the heated plasma for a time long enough to release energy in excess of that required to heat the plasma to reaction temperature and to maintain it thereat. The present invention is directed to the magnetic confinement of such plasma and finds particular utility in devices of this kind and their applications, including experimental devices and their use in experimentation and investigation related to plasma devices with toroidal discharges.
Several toroidal confinement plasma devices have been suggested and built. Most closely related to the present invention are: tokamak devices including divertor tokamaks, z-pinch devices including Reversed-Field-Pinch (RFP) devices; and spheromak devices, including those produced or sustained by z-pinch. In devices of this type, gas is confined in a toroidal region of the vessel and is heated to form a plasma which is generally held away from the walls of the vessel by appropriate magnetic fields. The topology of the vessel in such devices may be either toroidal (tokamak, RFP) or cylindrical (spheromaks), and these devices are generally axisymmetric. A topological torus/cylinder is any geometric solid figure that can be produced by an imaginary elastic deformation of an initial axisymmetric torus/cylinder. An axisymmetric torus has a hole, i.e. a region outside the toroidal volume, in the vicinity the rotational axis (major axis), whereas a cylinder is simply-connected, implying there is no such hole. An axisymmetric device is one in which all quantities are invariant to rotation about the rotational axis. A necessary condition for the magnetic confinement of plasma in a toroidal region is that there exist sets of nested toroidally closed magnetic surfaces in this region. A magnetic surface is defined as a mathematical surface, everywhere on which the magnetic field is tangential thereto. The magnetic surface enclosing zero volume in the center of a nest is called an elliptic magnetic axis. From the devices with a toroidal confinement region, those with toroidal vessel, called toroidal devices, ideally have only nested closed magnetic surfaces. Devices with open-ended vessel have, in addition, open magnetic surfaces which intersect the two end-surfaces of the topologically cylindrical vessel, in which case they have at least one separatrix, that is one magnetic surface separating the region of open magnetic surfaces from that of closed magnetic surfaces.
However, even for toroidal devices, it is sometimes found convenient to add a region with open magnetic surfaces, so as to produce a separatrix, having the role of an open-ended divertor. A divertor is a separatrix which establishes a transition between the set of magnetic nested toroidal surfaces and magnetic surfaces directed to the boundary. A divertor may have a profound influence on a plasma confinement device. Not only does it have as a primary effect, the isolation of the toroidal confinement plasma region from the surrounding region of the vessel by contributing to redirecting to the boundary impurities scraped off the wall, but it may also lead to an improved confinement state. This is illustrated by the so-called H-mode found in tokamaks, which is a regime of enhanced confinement, and requires almost always a divertor to be established. The presence of a divertor is also beneficial for ash-removal.
In some toroidal plasma confinement devices, the confining magnetic field includes magnetic field components produced by currents flowing through the confined plasma itself. However, in some of these devices, such as the tokamak, the toroidal field, much larger than the poloidal field, remains essentially produced by external means. External toroidal coils then determine the plasma equilibrium and avoid instabilities. On the other hand, in other devices, the toroidal field--of comparable amplitude to that of the poloidal field--is in great part, as in RFP, or entirely, as in spheromak, produced by the plasma current itself. The equilibrium is then reached at the outcome of a self-consistent process called plasma relaxation. These may be called therefore relaxation devices.
During relaxation, a plasma initially produced in an unstable state releases part of its free energy through a turbulent process till it reaches a lowest energy equilibrium state. Relaxation is a complex process of self-organization of a resistive plasma, which may involve substantial modification in its magnetic field, in particular in the topology of the magnetic surfaces. In its general behaviour, the relaxation process in relaxation devices seems to be quite well accounted for by J. B. Taylor's conjecture, Phys. Rev. Lett. 33 (1974), pp. 1139-1141. This conjecture states that very few magnetohydrodynamic (MHD) invariants from amongst the infinity of ideal MHD invariants holding for null resistivity, still hold on the time-scale of resistive relaxation. For the considered toroidal devices, the essential long-life invariant is global helicity, defined as: EQU H=.intg.A.B dV (1)
the integral being performed over the total volume of the toroidal vessel. A is any potential vector of B, satisfying V.times.A=B. For open-ended devices, the definition for helicity must be substituted by a less simple one, taking into account boundary effects. Remaining invariant on a large time-scale, helicity provides therefore a central constraint, determining the final equilibrium state. If this is the unique MHD invariant on large time-scals, then the relaxing plasma decays to the lowest energy state compatible with the geometry of the vessel and the value of H. This state may be shown to satisfy the equilibrium equation: EQU .mu..sub.o J=V.times.B=.mu.B (2)
where J is the current density, .mu..sub.o is the magnetic permeability at vacuum, and .mu. is a constant, independent of space, and has dimension of inverse length.
The physicality of the assumption that constant helicity plays a central role in modeling of relaxation has been largely confirmed by subsequent observations on prototypes built in different laboratories: RFP, multipinch, spheromaks.
In most relaxation devices, the only main additional magnetic constraint is the conservation of toroidal magnetic flux, for toroidal devices, or poloidal flux when externally imposed in open-ended devices. In such case, the stable equilibrium of the relaxed state is the solution of equation (2) with lowest .mu. among the possibly multiple solutions compatible with the values of the helicity, of the conserved flux and of the geometry of the vessel. Only that lowest energy solution, called the Taylor state, may be stable. Since no more free energy is available unless H is changed, the Taylor state is stable to ideal MHD instabilities, as well as to some resistive instabilities. However, the lowest energy solution is not necessarily the most favorable one for fusion application, in particular, as will be discussed below, when plasma pressure is taken into account. Yet the other equilibrium solutions of equation (2) are bound to decay unstably to the Taylor state, because, in present art relaxation devices, there is no additional constraint in the relaxation process to prevent this decay.
In certain MHD systems, however, there may be present an additional robust invariant of topological origin. This is a homotopic invariant, implying that it is insensitive to local change of topology of the magnetic surfaces, and that it may therefore be of comparable life-time to that of global helicity having a central role in modeling relaxation. Homotopy theory is the branch of topology which deals with the continuous deformations of fields. It should be distinguished from homeomorphy, which deals with the deformation of one surface into another. Homotopy, by contrast, determines whether one field configuration can be continuously deformed into another. The set of all configurations continuously deformable one into the other is called a homotopy class. Two configurations belonging to two different homotopic classes are not continuously deformable one into the other, and therefore one will not dynamically evolve into the other, which introduces an additional constraint. Conditions can be created in MHD systems where there is more than one homotopy class for the magnetic field, each class corresponding to a different value of a homotopic invariant. Existence of such systems was proved by Finkelstein, D. and Weil, D., International Journal of Theoretical Physics, Vol. 17, No. 3 (1978), pp. 201-217. In present art plasma relaxation devices, no device takes advantage of a magnetic homotopic invariant as a topological constraint in the relaxation. Yet, as already mentioned, from all the solutions of equation (2) for a given geometry, the lowest energy one is not necessarily the most favorable one in fusion reactor context, in particular with respect to the maximal plasma pressure tolerated by the magnetic configuration.
Equilibrium states obeying Equation (2) have no pressure gradient, because Vp=J.times.B. For practical purposes, real plasma must differ from Taylor state at least slightly, since real plasma must have finite pressure, and, actually, substantially high pressures are desired for fusion application. Such pressure is measured in terms of the quantity: ##EQU1## .beta. being the ratio of the mean plasma pressure to the mean magnetic pressure (here and throughout the remainder of this disclosure the system of units used is SI mks). For finite .beta., instabilities due to plasma pressure may arise, in particular the MHD interchange instabilities.
The MHD stability of a magnetically confined plasma with finite pressure is dependent on the pitch of the magnetic field lines encircling the magnetic axis. In toroidal plasma devices it is customary to use instead the safety factor q where: ##EQU2## this integration being performed, for axisymmetry, along close field lines of poloidal magnetic field B.sub.p. R is the distance from major axis and B.sub.p is the toroidal magnetic component.
In order to be MHD stable, toroidal plasma devices with finite pressure gradient must satisfy certain necessary conditions on q. In particular, if r is the mean minor radius of the toroidal surface, then: ##EQU3## must be large enough to satisfy relevant criteria including the Mercier criterion. s is the magnetic shear, which exerts a stabilizing effect on many classes of instabilities, particularly on MHD interchange instabilities.
It has been computed (C. M. Bishop, Nuclear Fusion 26 (1986), pp. 1063-1071) that stability to these interchanges is enhanced with the presence of a divertor, and that the stability properties become better as the poloidal null-point of the divertor is moved progressively towards the inside of the torus. Thus an inner divertor on the very inside may be the best operation for a toroidal confinement plasma device.
The most commonly used toroidal magnetic confinement configuration at present is the tokamak, whose principle defining characteristic is to achieve MHD stability requirements by supplying a sufficiently large toroidal magnetic field intensity B.sub.t, so as to be much higher (typically 5 to 10 times higher) than the poloidal magnetic field. The toroidal field must be provided by a large toroidal field coil system disposed around the confinement vessel. The theoretically predicted maximum .beta. is limited to be of the order of 0.10. Because of the small .beta. of the tokamak, fusion reactors based on this concept must either be large or must employ extraordinary high toroidal field strength.
Reversed-Field-Pinches (RFP) devices are most readily distinguished from tokamaks, which they superficially resemble, by being relaxation devices where the toroidal field is of approximate same amplitude as that of its poloidal field. As a consequence, a RFP device can achieve the same plasma density at much lower toroidal field than the tokamak. A recent review of the RFP art has been given by Bodin, H. A. B., Krakowski R. A., and Ortolani S., Fusion Technology 10 (1986), pp 307-353. The theory of relaxation under constant helicity accounts remarkably well for the universality of the RFP equilibrium states reached after relaxation. In particular, it is observed, as predicted by the theory, that for sufficiently high current densities, so that the product of .mu. by the the minor radius of the torus exceeds the critical value of 2.4, spontaneous reversal of the toroidal field at the edge of the plasma takes place. That is, the magnetic field component sensibly parallel to the magnetic axis has a direction in the outside region of the plasma opposite to its direction in the inner region, and as a result, g(r) passes through zero and changes sign near the boundary of the plasma. In general, the magnitude of q in the RFP remains everywhere substantially smaller than 1, but the shear is relatively high and, as a consequence, the maximal .beta. achievable in RFP devices is greater than in a tokamak. .beta..sub.p may be as high as 0.4. Fusion reactors based on the RFP concept can, therefore, either be smaller or use lower magnetic fields than with tokamaks.
However, the RFP device, as the tokamak, requires for its functioning toroidal field coils which link the plasma. The presence of this hard core at the center of the device introduces a most severe technological constraint in the practical design of such toroidal devices and it particularly complicates actual reactor design by requiring a toroidal blanket. In addition, the implementation of an inner poloidal divertor, considered as most suitable for enhanced stability and confinement, is rendered problematic by the presence of the hard core. In such toroidal devices, a divertor is introduced as an extraneous structure by additional coils. So far, several tokamaks have been built with poloidal divertors but none of them with an inner divertor. For RFP devices, most considered divertors divert the toroidal field, preserving the poloidal circular symmetry around the elliptic magnetic axis, and no RFP with inner poloidal divertor has been developed. The small-major radius side of these toroidal devices with inner hard core, for the RFP as well as for the tokamak, is already crowded and under high stress. An inner divertor would further complicate the design.
Other relaxation devices with toroidal region of confinement have been developed which do not involve an inner hard core. These bear the generic name of spheromaks. In a spheromak, the toroidal field is produced entirely by the plasma current. This has for an advantage obviating the requirement for the toroidal field coils. Unfortunately, the spheromak does not have high shear and it has been theoretically predicted to have small maximal .beta.. There are data suggesting that interchange instability is observable in contemporary spheromak experiments (see, in particular, Wysocki, F. J., et al., Physical Review Letters, Vol. 21, p. 2457 (1988). In the spheromak, there is no reversal of the toroidal field. The spheromak has a low shear because q varies between 0.8 and 0.7 in the classical spheromak, or between 0.8 and 0 in the spheromak with a hole. Some spheromaks have plasma on open field lines, yielding some kind of divertor, but no spheromak has a unique poloidal divertor situated in the innermost part of the toroidal region. The lack of reversal and the low shear, as well as the absence of an inner divertor, are linked to the fact that the lower energy Taylor states do not satisfy these properties and that there is no additional constraint to withhold decay to these Taylor states.